Problem 405

Determine whether to reject or fail to reject H_{0} at the level of significance of

(a)    α = 0.06.

(b)   α = 0.09.

H_{0};µ = 110,H_{a}: µ ≠ 110, and P = 0.0769.

 

 

Solution

 

(a)    Do  you reject or fail to reject H_{0} at the 0.06 level of significance?

When you assume the null hypothesis is true, a P-value of a hypothesis test is the probability of obtaining a sample statistic with a value as extreme or more extreme than the one determined from the sample data.

If the P-value is less then or equal to the level of significance, than reject H_{0}.If the P-valve is greater than the level of significance, then fail to reject H_{0}.

Fail to reject H_{0} because 0.0769 > 0.06.

 

(b)   Do you reject or fail to reject H_{0} at the 0.09 level of significance?

 

If the P-value is less than or equal to the level of significance, then reject H_{0}. If the P-value is greater then the level of significance, than fail to reject H_{0}.

 

Reject H_{0} because 0.0769 < 0.09.

 

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